https://file.aiquickdraw.com/mathbot/file/1726073893397zr8zy6x4.jpg

The system of equations given in the image is:

\[
\begin{aligned}
3x - 8y &= 4 \quad \text{(Equation 1)} \\
-5x + 6y &= 8 \quad \text{(Equation 2)}
\end{aligned}
\]

To solve this system, we can use either the substitution or the elimination method. Here, I'll use the elimination method.

### Step 1: Multiply the equations to eliminate one variable
Let's aim to eliminate \(x\). To do this, we need to make the coefficients of \(x\) in both equations equal. Multiply Equation 1 by 5 and Equation 2 by 3:

\[
\begin{aligned}
(5) \cdot (3x - 8y) &= (5) \cdot 4 \quad \Rightarrow \quad 15x - 40y = 20 \quad \text{(Equation 3)} \\
(3) \cdot (-5x + 6y) &= (3) \cdot 8 \quad \Rightarrow \quad -15x + 18y = 24 \quad \text{(Equation 4)}
\end{aligned}
\]

### Step 2: Add the equations to eliminate \(x\)

Now, add Equation 3 and Equation 4:

\[
(15x - 40y) + (-15x + 18y) = 20 + 24
\]

Simplifying:

\[
0x - 22y = 44 \quad \Rightarrow \quad -22y = 44
\]

### Step 3: Solve for \(y\)

\[
y = \frac{44}{-22} = -2
\]

### Step 4: Substitute \(y = -2\) into one of the original equations

Substitute \(y = -2\) into Equation 1:

\[
3x - 8(-2) = 4 \quad \Rightarrow \quad 3x + 16 = 4
\]

Now, solve for \(x\):

\[
3x = 4 - 16 \quad \Rightarrow \quad 3x = -12 \quad \Rightarrow \quad x = \frac{-12}{3} = -4
\]

### Solution:
The solution to the system of equations is:
\[
x = -4, \quad y = -2
\]

Would you like more details on any part of this solution, or do you have further questions?

---

Here are 5 related questions to explore:

1. What is the substitution method for solving systems of equations, and how does it differ from elimination?
2. How can you verify the solution to a system of equations?
3. What happens if a system of equations has no solution or infinitely many solutions?
4. Can systems of equations be solved graphically, and how does this compare to algebraic methods?
5. What is a real-world example where systems of equations might be applied?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations.

Solve the system of equations: 3x - 8y = 4 and -5x + 6y = 8

Learn how to solve the system of linear equations 3x - 8y = 4 and -5x + 6y = 8 using the elimination method. This step-by-step solution explains key algebraic concepts, including how to eliminate variables and solve for x and y. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation